Supervisors: Stef van Buuren and Gerko Vink | Mentor: Daniela Cianci
\[\begin{align} B&=\frac{T}{M-1} \sum_{m=1}^{M}\left(\bar{\theta}^{(\cdot m)}-\bar{\theta}^{(\cdot \cdot)}\right)^{2}, \quad \text{where} \quad \bar{\theta}^{(\cdot m)}=\frac{1}{T} \sum_{t=1}^{T} \theta^{(t m)}, \\ &\quad \text{ and } \quad \bar{\theta}^{(\cdot \cdot)}=\frac{1}{M} \sum_{m=1}^{M} \bar{\theta}^{(\cdot m)} \\ W&=\frac{1}{M} \sum_{m=1}^{M} s_{j}^{2}, \quad \text{where} \quad s_{m}^{2}=\frac{1}{T-1} \sum_{t=1}^{T}\left(\theta^{(t m)}-\bar{\theta}^{(\cdot m)}\right)^{2} \\ \widehat{R}&=\sqrt{\frac{\widehat{\operatorname{var}}^{+}(\theta | y)}{W}}, \quad \text{where} \quad \widehat{\operatorname{var}}^{+}(\theta | y)=\frac{N-1}{N} W+\frac{1}{N} B. \end{align}\]
Chang, Winston, Joe Cheng, JJ Allaire, Yihui Xie, and Jonathan McPherson. 2017. “Shiny: Web Application Framework for R.” https://CRAN.R-project.org/package=shiny.
R Core Team. 2019. R: A Language and Environment for Statistical Computing. Vienna, Austria. https://www.R-project.org/.
Van Buuren, Stef. 2018. Flexible Imputation of Missing Data. Chapman; Hall/CRC.
Van Buuren, Stef, and Karin Groothuis-Oudshoorn. 2011. “Mice: Multivariate Imputation by Chained Equations in R.” Journal of Statistical Software 45 (1): 1–67. https://doi.org/10.18637/jss.v045.i03.
Vehtari, Aki, Andrew Gelman, Daniel Simpson, Bob Carpenter, and Paul-Christian Bürkner. 2019. “Rank-Normalization, Folding, and Localization: An Improved $\widehat{R}$ for Assessing Convergence of MCMC,” March. http://arxiv.org/abs/1903.08008.